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NHL Pythagorean Luck through December 10, 2015
*December 11, 2015*

*Posted by tomflesher in Hockey, Sports.*

Tags: hockey, NHL, Pythagorean expectation, wins above expectation

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Tags: hockey, NHL, Pythagorean expectation, wins above expectation

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Below is a plot of NHL teams’ Pythagorean luck through games played on December 10. The bubbles are scaled to the number of wins each team has.

Shockingly, the 12-16 Calgary Flames are 2.4 wins above their expectation, meaning that they should really be a 10-18 or 9-19 team right now. Meanwhile, the Canucks are suffering at 3.4 wins below expectation; at 11-19, they could easily be a .500 team if a few pucks had bounced differently.

Lucky wins for each team follow:

Team |
Lucky Wins |

Dallas Stars | 2.97 |

Montreal Canadiens | -1.23 |

Washington Capitals | 1.58 |

New York Rangers | -1.24 |

Los Angeles Kings | 1.38 |

New York Islanders | -0.77 |

Detroit Red Wings | 1.09 |

St. Louis Blues | 1.08 |

Nashville Predators | 0.30 |

Ottawa Senators | -0.21 |

Chicago Blackhawks | -0.29 |

Boston Bruins | -0.60 |

Minnesota Wild | -0.23 |

Florida Panthers | -0.93 |

Pittsburgh Penguins | 1.28 |

New Jersey Devils | -0.66 |

Tampa Bay Lightning | -1.65 |

Philadelphia Flyers | 1.41 |

Winnipeg Jets | 0.58 |

Vancouver Canucks | -3.40 |

San Jose Sharks | 0.39 |

Anaheim Ducks | 0.13 |

Arizona Coyotes | 1.50 |

Edmonton Oilers | -0.19 |

Calgary Flames | 2.40 |

Buffalo Sabres | -1.26 |

Toronto Maple Leafs | -1.58 |

Colorado Avalanche | -1.38 |

Carolina Hurricanes | 0.23 |

Columbus Blue Jackets | -0.70 |

League Average | 0.00 |

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Exactly how big an impact have those trades had?
*August 26, 2015*

*Posted by tomflesher in Baseball.*

Tags: bullpen, Pythagorean luck, trades, wins above expectation

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Tags: bullpen, Pythagorean luck, trades, wins above expectation

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The Mets made some huge deals near the trade deadline to pick up **Juan Uribe** and **Kelly Johnson** on July 25, **Tyler Clippard** on July 28, and **Yoenis Cespedes** on August 1. (Those are the dates of the first games the players appeared in for the Mets.) Let’s take a look at the effects of those trades. If there was no effect from the trades, then the Mets’ improvement would have to be basically indistinguishable from chance.

**April:**The Mets scored 97 runs and and allowed 81 for a 16-run differential and a .581 Pythagorean expectation. They went 15-8 for a win percentage of .652, giving them a Pythagorean differential of .071 and 1.63 Wins Above Expectation.^{1}**May:**95 runs scored, 105 allowed, 11-14, for an expected .455 winning percentage, .440 actual winning percentage, -.015 differential and -.36 WAE.**June:**84 runs scored, 105 allowed, 9-15, for an expected .413, actual .375, -.038 differential and -.90 WAE.**July:**89 runs scored, 83 allowed, 11-12, for an expected .532, realized .478, -.053 differential and -1.23 WAE.**August:**137 runs scored, 84 allowed, 16-5, for an expected .709, actual .762, .053 differential and 1.11 WAE.

Clearly, the jump in August has been enormous, especially since they only played 21 games in August; in fact, the Mets averaged 3.76 runs per game through July, but 8.2 in August. In fact, if we start on July 25, the Mets have averaged 9.26 runs per game. Between Uribe, Johnson, and Cespedes, that’s a huge improvement – five and a half runs per game!

What about Clippard? Well, for one, the Mets averaged 3.9 runs allowed through July; since August 1, we’re at 4.0. However, Clippy’s ERA with the Mets is 1.93, and the bullpen ERA overall is 3.08. The August ERA for the bullpen has been an alarming 3.59, but that includes the hilarious trip to Colorado, too. That makes Tyler’s low ERA even more impressive. (For the record, future Mets closer **Hansel Robles** has a 3.27 August ERA – that’s 4 ER in 11.0 IP – and current closer **Jeurys Familia** hasn’t allowed a run in 11 1/3 innings pitched in August.) Clippy’s definitely value-added in the bullpen, especially considering that the alternative might be **Dario Alvarez** or **Dillon Gee** unhappy in his role.

Most notably, though, since the Mets picked up Uribe and Johnson, their wins above expectation have been statistically zero. They’ve been playing to their potential, not above it, since July 25.

We’re in for an interesting end to the year.

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^{1} Pythagorean differential is computed as (Winning percentage – Pythagorean Expectation). Wins Above Expectation is computed as Pythagorean differential times games played. They measure the same concept but are scaled differently.

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June Wins Above Expectation
*July 1, 2011*

*Posted by tomflesher in Baseball, Economics.*

Tags: Baseball, baseball-reference.com, statistics, wins above expectation

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Tags: Baseball, baseball-reference.com, statistics, wins above expectation

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Even though I’ve conjectured that team-level wins above expectation are more or less random, I’ve seen a few searches coming in over the past few days looking for them. With that in mind, I constructed a table (with ample help from Baseball-Reference.com) of team wins, losses, Pythagorean expectations, wins above expectation, and Alpha.

Quick definitions:

- The
**Pythagorean Expectation (pyth%)**is a tool that estimates what percentage of games a team should have won based on that team’s runs scored and runs allowed. Since it generates a percentage,**Pythagorean Wins (pythW)**are estimated by multiplying the Pythagorean expectation by the number of games a team has played. **Wins Above Expectation (WAE)**are wins in excess of the Pythagorean expected wins. It’s hypothesized by some (including, occasionally, me) that WAE represents an efficiency factor – that is, they represent wins in games that the team “shouldn’t” have won, earned through shrewd management or clutch play. It’s hypothesized by others (including, occasionally, me) that WAE represent luck.**Alpha**is a nearly useless statistic representing the percentage of wins that are wins above expectation. Basically, W-L% = pyth% + Alpha. It’s an accounting artifact that will be useful in a long time series to test persistence of wins above expectation.

The results are not at all interesting. The top teams in baseball – the Yankees, Red Sox, Phillies, and Braves – have either negative WAE (that is, wins below expectation) or positive WAE so small that they may as well be zero (about 2 wins in the Phillies’ case and half a win in the Braves’). The Phillies’ extra two wins are probably a mathematical distortion due to **Roy Halladay**‘s two tough losses and two no-decisions in quality starts compared with only two cheap wins (and both of those were in the high 40s for game score). In fact, Phildaelphia’s 66-run differential, compared with the Yankees’ 115, shows the difference between the two teams’ scoring habits. The Phillies have the luxury of relying on low run production (they’ve produced about 78% of the Yankees’ production) due to their fantastic pitching. On the other hand, the Yankees are struggling with a 3.53 starters’ ERA including **Ivan Nova** and AJ Burnett, both over 4.00, as full-time starters. The Phillies have three pitchers with 17 starts and an ERA under 3.00 (Halladay, **Cliff Lee**, and **Cole Hamels**) and **Joe Blanton**, who has an ERA of 5.50, has only started 6 games. Even with Blanton bloating it, the Phillies’ starer ERA is only 2.88.

That doesn’t, though, make the Yankees a badly-managed team. In fact, there’s an argument that the Yankees are MORE efficient because they’re leading their league, just as the Phillies are, with a much worse starting rotation, through constructing a team that can balance itself out.

That’s the problem with wins above expectation – they lend themselves to multiple interpretations that all seem equally valid.

Tables are behind the cut. (more…)

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Is ‘luck’ persistent?
*May 25, 2011*

*Posted by tomflesher in Baseball, Economics.*

Tags: American League, Baseball, Pythagorean expectation, wins above expectation

2 comments

Tags: American League, Baseball, Pythagorean expectation, wins above expectation

2 comments

I’ve been listening to Scott Patterson’s The Quants in my spare time recently. One of the recurring jokes is Wall Street traders’ use of the word ‘Alpha’ (which usually represents abnormal returns in finance) to refer to a general quality of being skillful or having talent. That led me to think about an old concept I haven’t played with in a while – wins above expectation.

As a quick review, wins above expectation relate a team’s actual wins to its Pythagorean expectation. If the team wins more than expected, it has a positive WAE number, and if it loses more than expected, it has wins below expectation, or, equivalently, a negative WAE. It’s tempting to think of WAE as representing a sort of ‘alpha’ in the traders’ sense – since the Pythagorean Expectation involves groups of runs scored and runs allowed, it generates a probability that a team with a history represented by its runs scored/runs allowed stats will win a given game. If a team has a lot more wins than expected, it seems like that represents efficiency – scoring runs at crucial times, not wasting them on blowing out opponents – or especially skillful management. Alternatively, it could just be luck. Is there any way to test which it is?

It’s difficult. However, let’s break down what the efficiency factor would imply. In general, it would represent some combination of individual player skill (such as the alleged clutch hitting ability) and team chemistry, whether that boils down to on- or off-field factors. Assuming rosters don’t change much over the course of the year, then, efficiency also shouldn’t change much over the course of the year. Similarly, if a manager’s skill was the primary determinant of wins above expectation, then for teams that don’t change managers midyear, we wouldn’t expect much of a change throughout the course of the season. Most managers work up through the minors, so there probably isn’t a major on-the-job training effect to consider.

On the other hand, if wins above expectation are just luck, then we wouldn’t need to place any restrictions on them. Maybe they’d change. Maybe they wouldn’t. Who knows?

In order to test that idea, I pulled some data for the American League off Baseball Reference from last season. I split the season into pre- and post-All-Star Break sets and calculated the Pythagorean expectation (using the 1.81 exponent referred to in Wikipedia) for each team. I found WAE for each team in each session, then found each team’s ‘Alpha’ for that session by dividing WAE by the number of games played. Basically, I assumed that WAE represented extra win probability in some fashion and assumed it existed in every game at about the same level. The results:

As is evident from the table, a whopping 10 out of the 14 teams see a change in the sign of Alpha from before the All-Star Game to after the All-Star Game. The correlation coefficient of Alpha from pre- to post-All-Star is -.549, which is a pretty noisy correlation. (Note also that this very closely describes regression to the mean.) It’s not 0, but it’s also negative, implying one of two things: Either teams become less efficient and/or more badly managed, on average, after the break, or Alpha represents very little more than a realization of a random process, which might just as well be described as luck.

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June 15 Wins Above Expectation
*June 16, 2010*

*Posted by tomflesher in Baseball.*

Tags: Angels, Baseball, Rays, Tigers, wins above expectation

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Tags: Angels, Baseball, Rays, Tigers, wins above expectation

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Wins Above Expectation are a statistic determined using team wins and the Pythagorean expectation, which is in turn determined using runs scored by and against each team. The Pythagorean expectation is the proportion of runs scored squared to runs scored squared plus runs against squared. It’s interpreted as an expected winning percentage.

Wins Above Expectation (WAE) is then the difference between Wins and Expected Wins, which are simply the Pythagorean Expectation multiplied by Games played. It’s a useful measure because it can be interpreted as wins that are due to efficiency (in economic terms) or, more simply, play that’s some combination of smart, clutch, and non-wasteful. It rewards winning close games and penalizes teams that win lots of laughers but lose close games, since the big wins predict more games will be won when all those runs are spent winning only one game.

Using Baseball-Reference.com, I crunched the numbers for AL teams up to June 15. As usual, the Los Angeles Angels of Anaheim lead the league in WAE with 3.68, with Detroit’s 2.39 a close second, but the Tampa Bay Rays are a surprising last with -1.96 WAE. Obviously, this early in the season it’s too soon to conclude anything based on this, but the complete data is behind the cut. (more…)

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How Useful is the Pythagorean Expectation?
*May 18, 2010*

*Posted by tomflesher in Baseball.*

Tags: baseball-reference.com, one-game playoffs, Pythagorean expectation, wins above expectation

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Tags: baseball-reference.com, one-game playoffs, Pythagorean expectation, wins above expectation

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The Pythagorean expectation is a method used to approximate how many wins a baseball team “should” have based on its offense (runs scored) and its defense (runs allowed). As the linked article points out, there are some problems with the formula. As far as I’m concerned, the most useful application of an expected win percentage is to compare teams that are otherwise similar. Let’s say, for example, that I have two teams that have identical records and I want to predict which team will win an upcoming series. In that case, an expected win percentage would be useful to indicate which team has more firepower over time.

What’s the perfect way to test this? One-game playoffs. Behind the cut, I have the results of some number-crunching I did to test whether the Pythagorean expectation generates useful results.